Ramps

1. Ramps

4. Observations About Ramps • It’s difficult to lift a heavy cart straight up • It’s easer to push a heavy cart up a ramp • The ease depends on the ramp’s steepness • Gradual ramps involve gentler pushes • Gradual ramps involve longer distances

5. 4 Questions about Ramps • Why doesn’t the cart fall through the ramp? • Are both cart and ramp pushing on each other? • Why is it easier to push the cart up a ramp? • Is there a physical quantity that’s the same for any trip up the ramp, regardless of its steepness?

6. Question 1 • Why doesn’t the cart fall through the ramp? • Why doesn’t a ball fall through a table? • Is the table pushing up on the ball?

7. Support Forces • A support force • prevents the ball from penetrating the table’s surface • points directly away from the table’s surface • Forces along surface are friction (ignore for now)

9. Net Force • The net force on the ball is • the sum of all forces on that ball • responsible for the ball’s acceleration

10. Adding up the Forces • As it sits on the table, the ball experiences • its weight downward • a support from the table upward • Since the ball isn’t accelerating, • the sum of forces (i.e., net force) on the ball is zero • the support force must balance ball’s weight! • Since cart isn’t accelerating into ramp, • the ramp’s support force must keep cart on surface

11. Question 2 • Are both cart and ramp pushing on each other? • Are both ball and table pushing on each other? • Is the table pushing on the ball? • Is the ball pushing on the table? • Which is pushing harder?

12. An Experiment • If you push on a friend, will that friend always push back on you? • Yes • No

13. Newton’s Third Law • For every force that one object exerts on a second object, there is an equal but oppositely directed force that the second object exerts on the first object.

14. Forces Present (Part 1) • For the ball resting on the table, the forces are • On ball due to gravity (its weight) • On ball due to support from table • On table due to support from ball • These forces all have the same magnitude • Where is the other 3rd law pair? zero acceleration 3rd lawpair

15. Forces Present (Part 2) • On earth due to gravity from the ball • On ball due to gravity from the earth • On ball due to support from table • On table due to support from ball • Forces 2 and 3 aren’t a Newton’s 3rd law pair! • when equal in magnitude, ball doesn’t accelerate • when not equal in magnitude, ball accelerates! 3rd lawpair 3rd lawpair

16. Two Crucial Notes: • While the forces two objects exert on one another must be equal and opposite, the net force on each object can be anything. • Each force within an equal-but-opposite pair is exerted on a different object, so they don’t cancel directly.

17. Question 3 • Why is it easier to push the cart up a ramp? • How hard must you push on the cart?

18. Forces on a Cart on a Ramp • If you balance ramp force, cart won’t accelerate support force ramp force (sum) weight

20. Balanced Cart on Ramp • If you balance the ramp force, • the cart won’t accelerate • the cart will coast – at rest, uphill, or downhill • The more gradual the ramp, • the more nearly weight and support balance • the smaller the ramp force on the cart • the easier it is to balance the ramp force!

21. Question 4 • Is there a physical quantity that’s the same for any trip up the ramp, regardless of its steepness? • What physical quantity is the same for • a long trip up a gradual ramp • a medium-long trip up a steep ramp • a short trip straight up a vertical ramp

23. Energy and Work • Energy – a conserved quantity • can’t be created or destroyed • can be transformed or transferred between objects • is the capacity to do work • Work – mechanical means of transferring energy work = force · distance (where force and distance in same direction)

24. Work Lifting a Cart (Part 1) • Going straight up: • Forceis large • Distanceis small work = Force · Distance

25. Work Lifting a Cart (Part 2) • Going up ramp: • Force is small • Distance is large work = Force · Distance

26. Work Lifting a Cart (Part 3) • Going straight up: work = Force · Distance • Going up ramp: work = Force · Distance • The work is the same, either way!

27. Mechanical Advantage • Mechanical advantage • Doing the same amount of work • Redistributing force and distance • A ramp provides mechanical advantage • You can raise a heavy cart with a modest force • You must push that cart a long distance • Your work is independent of the ramp’s steepness

28. The Transfer of Energy • Energy has two principal forms • Kinetic energy – energy of motion • Potential energy – energy stored in forces • Your work transfers energy from you to the cart • You do work on the cart • Your chemical potential energy decreases • The cart’s gravitational potential energy increases

29. Summary about Ramps • Ramp supports most of the cart’s weight • You can easily balance the remaining ramp force • You do work pushing the cart up the ramp • Your work is independent of ramp’s steepness • The ramp provides mechanical advantage • It allows you to push less hard • but you must push for a longer distance